Question 410568
{{{ (6/x-2)-(3/x)=(-5/x-4)}}}
Multiply both sides by {{{x*(x-2)*(x-4)}}}
{{{6*x*(x-4) - 3*(x - 2)*(x - 4) = (-5)*x*(x - 2)}}}
{{{6x^2 - 24x - 3*(x^2 - 2x - 4x + 8) = -5x^2 + 10x}}}
{{{ 6x^2 - 24x - 3x^2 + 6x + 12x - 24 = -5x^2 + 10x}}}
{{{3x^2 - 6x - 24 = -5x^2 + 10x}}}
{{{8x^2 - 16x - 24 = 0}}}
{{{x^2 - 2x - 3 = 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{a = 1}}}
{{{b = -2}}}
{{{c = -3}}}
{{{x = (-(-2) +- sqrt( (-2)^2-4*1*(-3) ))/(2*1) }}} 
{{{x = ( 2 +- sqrt( 4 + 12 ))/ 2 }}} 
{{{x = ( 2 + 4)/ 2 }}}
{{{x = 3}}}
and
{{{x = ( 2 - 4)/ 2 }}}
{{{x = -1}}}
I'll check for {{{x = -1}}}
{{{ (6/x-2)-(3/x)=(-5/x-4)}}}
{{{ (6/(-1-2))-(3/(-1))=(-5/(-1)-4)}}}
{{{ -2 + 3 = -5/(-5)}}}
{{{1 = 1}}}
OK